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Rounding off decimals - class-VII

Description: rounding off decimals
Number of Questions: 35
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Tags: reviewing number concepts decimal fractions real numbers decimals maths number systems number system fractions and standard forms
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Write the number of significant digits in:

$3.005$.

  1. $4$

  2. $2$

  3. $1$

  4. $0$


Correct Option: A
Explanation:

Zeroes placed between other digits are always significant.
$\therefore  3.005$ has $4$ significant digits.

Write the number of significant digits in:

$5.16 \times 10^8$.

  1. $3$

  2. $1$

  3. $2$

  4. $9$


Correct Option: A
Explanation:

$5.16\times 10^8$
There are $3$ significant figures. When a number is  written in scientific notation, only significant figures are placed into the numerical portion.


Write the number of significant digits in:

$16.000$.

  1. $2$

  2. $5$

  3. $16$

  4. $1$


Correct Option: B
Explanation:

All zeroes which are both to the right of the decimal point and to the right of all non-zero significant digits are themselves significant.
$\therefore  16.000$ has $5$
significant digits

Write the number of significant digits in $23.4$

  1. $2$

  2. $23.4$

  3. $3$

  4. $1$


Correct Option: C
Explanation:

Non-zero digits are always significant.

$\therefore  23.4$ has $3$
significant digits.

Divide $7$  by $11$ and express the result in two significant digits.

  1. $0.64$

  2. $0.583$

  3. $0.54$

  4. $0.67$


Correct Option: A
Explanation:

On dividing 7 by 11, we get 0.6363636363.... .

If we have to express this in two significant digits, then it would be 0.64 as 6 is > 5  and 1 would get added to 3.

Write the number of significant digits in:

$0.07$.

  1. $7$

  2. $1$

  3. $3$

  4. $2$


Correct Option: B
Explanation:

Zeroes placed before other digits are not significant.
$\therefore  0.07$
has $1$ significant digit.

Write the number of significant digits in:

$0.0016$.

  1. $2$

  2. $5$

  3. $1$

  4. $4$


Correct Option: A
Explanation:

Zeroes placed before other digits are not significant.
$\therefore  0.0016$  has $2$ significant digits.

Write the number of significant digits in:

$805.060$.

  1. $3$

  2. $2$

  3. $5$

  4. $6$


Correct Option: D
Explanation:

All zeroes which  are both to the right of the decimal point and to the right of all non-zero significant digits  are themselves significant.
$\therefore  805.060$ has $6$
significant digits

For rational numbers, $x$ and $y,$ if $x > y,$ then which of the following is always a positive rational number?

  1. $ y - xy$

  2. $ xy-x$

  3. $ y-x$

  4. $ x- y $


Correct Option: D
Explanation:
If $x>y$

$y-xy\rightarrow $ can be both positive and negative.

Example coside $x>1$ & $y>0$

$\left(y-xy\right)<0$

$xy-x\rightarrow $ can be both positive and negative 

$y-x\rightarrow $ always negative

$\boxed {x-y\rightarrow always\ positive\ since\ x>y}$

$0.\overline{5}$ in the form of $\frac{p}{q}$ is :

  1. $\dfrac{9}{5}$

  2. $\dfrac{5}{10}$

  3. $\dfrac{5}{9}$

  4. $\dfrac{10}{5}$


Correct Option: C
Explanation:

$Let\quad x=.555....\ On\quad multiplying\quad by\quad 10\quad on\quad both\quad sides\quad \ 10x=5.555....\ On\quad subtracting\quad both\quad equations\quad \ 9x=5\ x=\dfrac { 5 }{ 9 } \ $

Hence, correct answer is option C.

If $x$ and $y$ are positive real number, then which of the following is correct?

  1. $x > y \Rightarrow -x > -y $

  2. $x > y \Rightarrow -x < -y $

  3. $x > y \Rightarrow \dfrac{1}{x} > \dfrac{1}{y} $

  4. $x > y \Rightarrow \dfrac{1}{x} < \dfrac{-1}{y} $


Correct Option: B
Explanation:

If $x$ and $y$ are positive number and $x>y$, then 

$\Rightarrow -x<-y$ 
Also, $x>y$ $\Rightarrow \dfrac{1}{x}<\dfrac{1}{y}$
Hence, B is correct option.

Express $\displaystyle 9\frac{7}{20}$ as a decimal.

  1. $9.05$

  2. $9.53$

  3. $9.26$

  4. $9.35$


Correct Option: D
Explanation:

$9\dfrac{7}{20}= \dfrac{187}{20}=9.35$

Hence the correct answer is option D.

In expressing a length $81.472 \ km$ as nearly as possible with three significant digits, the percent error is

  1. $0.34\%$

  2. $0.034\%$

  3. $0.0034\%$

  4. $0.0038\%$


Correct Option: B
Explanation:

$81.472 km = 81472$ meters $= 81500$ meters with three significant digits.
$\displaystyle \therefore Error\%=\frac{81500-81472}{81472}\times 100=0.034\%$

If $a, b, c$ are distinct $+ve$ real numbers and ${ a }^{ 2 }+{ b }^{ 2 }+{ c }^{ 2 }=1$ then $ab + bc + ca$ is 

  1. less then $1$

  2. equal to $1$

  3. greater then $1$

  4. any real no.


Correct Option: A
Explanation:

${a}^{2} + {b}^{2} + {c}^{2} = 1 \quad \left( \text{Given} \right)$


${\left( a +  b + c \right)}^{2} > 0$

${a}^{2} + {b}^{2} + {c}^{2} + 2 \left( ab + bc + ca \right) > 0$

$1 + 2 \left( ab + bc + ca \right) > 0$

$2 \left( ab + bc + ca \right) > -1$

$\Rightarrow ab + bc + ca >-\dfrac 12$

If the decimal o.d25d25d25 ................ is expressible in the form n/27, then d+n must be

  1. 9

  2. 28

  3. 30

  4. 34


Correct Option: D
Explanation:

$x = 0.d25 d25d25 -----$
$x = 0.\overline{d25}$
$1000 x = d25. \overline{d25}$
$999 x = d 25$
$x = \displaystyle \frac{d 25}{999}$
$x = \displaystyle \frac{d25}{37.27}$
take d = 9 then $x = \displaystyle \frac{25}{27}$
$d = 9          n = 25$
$d + n = 34$

Express $ \dfrac {5}{13} $ correct to $3$ significant figures.

  1. $1.26$

  2. $0.385$

  3. $0.00385$

  4. $0.103$


Correct Option: B
Explanation:

$\dfrac {5}{13} = 0.3846$


Rounding off to $3$ places to nearest decimal, we get $0.385$.
So, option $B$ is correct.

A $3$ digit id a $3$ digit number (not starting with zero) which reads the same backwards as forwards. For example $171$. The sum of all even $3$ digit palindromes, is 

  1. $22380$

  2. $25700$

  3. $22000$

  4. $22400$


Correct Option: A

The number of significant digits in the measurement of the side of a square whose computed area is $1.1025$ square inches to the nearest tenthousandth of a square cm is

  1. $2$

  2. $3$

  3. $4$

  4. $5$

  5. $1$


Correct Option: D
Explanation:

(d) is the correct choice.

Which of the following statements is incorrect regarding significant figures?

  1. All the non-zero digits are significant.

  2. All the zeros between two non-zero digits are significant.

  3. Greater the number of significant figures in a measurement, smaller is the percentage error.

  4. The power of 10 is counted while counting the number of significant figures.


Correct Option: D
Explanation:

The term significant figures are referring to the number of important digits (0 through 9 inclusive) in the coefficient of some expression in the scientific notation. The number of significant figures in any expression indicate the confidence or precision with which we can state a quantity.

Some rules for significant figures are:

1. All non-zero numbers are significant.

2. Zeros located between non-zero digits are significant.

3. Trailing zeros at the end will be significant only if the number contains a decimal point; otherwise, they are insignificant.

4. Zeros to the left of the first nonzero digit are insignificant.

5. Number in exponents (for example power of 10) is insignificant.

Thus option D is correct. 

Divide $0.3297$ by $0.07$, correct to $2$ significant digits.

  1. $4.4$

  2. $4.7$

  3. $4.9$

  4. None of these


Correct Option: B
Explanation:

$0.3297 \div 0.07 = 4.71$

as the digit in ten's place is not greater than 5, it cannot be replaced.
$\therefore 0.3297 \div 0.07 = 4.7$

In the decimal, $2.4d7$, $d$ represents a digit from 0 to 9. If the value of the decimal rounded to the nearest tenth, is less than $2.5$, what are the possible values of $d$?

  1. $0,1,2$

  2. $0,1,2,3,4$

  3. $5,6,7$

  4. $5,6,7,8,9$


Correct Option: B
Explanation:

The correct answer is ${0,1,2,3,4}$.

: If $d \ge 5$, the decimal rounded to the nearest tenth will be greater than $2.5$.
Hence, option B is correct.

$\displaystyle 6.743\times 100$ is equal to _____ 

  1. $674.300$

  2. $.674300$

  3. $67.4300$

  4. $6.74300$


Correct Option: A
Explanation:

The number of decimal places from the right of the number in the question will be in the product at the same number of places.

$6.743×100=674.300$   ($3$ decimal places)
So option A is the correct answer.

Calculate the value of the following expression by appropriate rounding off of the numbers:
$\displaystyle 0.43\times 0.87=$

  1. $0.31$

  2. $0.35$

  3. $0.36$

  4. $0.38$


Correct Option: C
Explanation:
Since in the case of $0.43$, the last digit is less than $5$, it would be rounded off to $0.4$
Likewise, since the last digit of $0.87$ is greater than $5$, it would be rounded off to $0.9$
$0.43 \times 0.87$ thus becomes $0.4 \times 0.9 = 0.36$

On rounding off the decimal part of $32.4$ to the nearest one, we get

  1. $30$

  2. $32$

  3. $33$

  4. $35$


Correct Option: B
Explanation:

In $32.4$, digit $4$ is less than $5$ so we will round off to $32.$
After rounding of $32.4$ will become $32.$

While rounding off, if the digit to be dropped is less than $5$, then the preceding digit:

  1. increases by $1$

  2. remains unchanged

  3. decreases by $1$

  4. None of the above


Correct Option: B
Explanation:
When rounding, you examine the digit following (i.e., to the right of) the digit that is to be the last digit in the rounded off number. The digit you are examining is the first digit to be dropped.

  1. If that first digit to be dropped is less than $5$ (that is, $1, 2, 3 $ or $4$), drop it, and also drop all the digits to the right of it.
  2. If that first digit to be dropped is more than $5$ (that is, $6, 7, 8$ or $9$), increase by 1 the number to be rounded, that is, the preceeding digit (to the digit being dropped).
Thus, in our case, since the digit to be dropped is less than $5$, we make no change to the preceding digit. 

Sohan wishes to order salt for himself, but the salt is only sold in $30$-pound bags. He currently has $75$ pounds of salt, and he needs to have a minimum of $200$ pounds. Determine the inequality which shows the possible values for the number of bags, b, that Macro needs to order in order to meet his minimum requirement.

  1. $\displaystyle b\ge 4$

  2. $\displaystyle b\ge 5$

  3. $\displaystyle b\ge 6$

  4. $\displaystyle b\ge 7$


Correct Option: B
Explanation:

Sohan needs to have $200$ pounds but he currently has $75$ pounds

And bags sold only $30$ pounds bag.
Then sohan take bags in $75$ pounds $=$ $\dfrac{75}{30}=2.5$ says 2
But he needed bages in $200$ pounds $=$ $\dfrac{200}{30}=6.67$ says 7
Then the inequality of number of bags (b) $=6.67-2.5=4.16$ says $5$
Hence, option B is correct.

66.7 can be approximated to

  1. 67

  2. 92

  3. 88

  4. 127


Correct Option: A
Explanation:

Given 66.7

As we can see number after decimal is more than 5 so approximated value is 67

Choose the correct alternative.
If $\bar {d}=-20.83,\bar {x}=254.17$, then $A=?$

  1. $270$

  2. $275$

  3. $233.34$

  4. $12.20$


Correct Option: A

List T consists of 30 positive decimals, none of which is an integer, and the sum of the 30 decimals is S.The estimated sum of the 30 decimals, E, is defined as follows. Each decimal in T whose tenths digit is even is rounded up to the nearest integer, and each decimal in T whose tenths digit is odd is rounded down to the nearest integer; E is the sum of the resulting integers. If $\displaystyle \frac { 1 }{ 3 } $ of the decimals in T have a tenths digit that is even, which of the following is a possible value of E- S ? 
I. -16
II. 6
III.10

  1. I only

  2. I and II only

  3. I and III only

  4. II and III only

  5. I, II and III


Correct Option: B

Find the value to three places of decimal of  the following. It is given that $\sqrt{2}=1.414, \sqrt{3} = 1.732, \sqrt{5} = 2.236$ and $\sqrt{10}=3.162.$ 


$\dfrac{\sqrt{5}+1}{\sqrt{2}}$

  1. $2.288$

  2. $1.2845$

  3. $3.629$

  4. None of the above


Correct Option: A
Explanation:
Given,

$\dfrac {\sqrt 5+1}{\sqrt {2}}$

$=\dfrac {2.236+1}{1.414}$

$=2.288$

What is $4,563,021 \div 10^5$, rounded to the nearest whole number?

  1. 45

  2. 44

  3. 46

  4. 47


Correct Option: C
Explanation:

To divide by a positive power of 10, shift the decimal point to the left. This yields 45.63021. To round to the nearest whole number, look at the tenths place. The digit in the tenths place, 6, is more than 5. Therefore, the number is closest to 46.

Round off each of the following as required.

$5.5493$ correct to two decimal places.

  1. $5.00$

  2. $5.54$

  3. $5.50$

  4. $5.55$


Correct Option: D
Explanation:

As the third digit is greater than $5$, the second digit $4$ can be rounded to $5$.
Thus, rounding off $5.5493$ gives $5.55$.

The correct expansion of $6.\overline {46}$ in the fractional form is :

  1. $\dfrac{646}{99}$

  2. $\dfrac{640}{100}$

  3. $\dfrac{64640}{1000}$

  4. $\dfrac{640}{99}$


Correct Option: D
Explanation:

$6.\overline {46} = 6+ \overline {46}= 6+\dfrac{46}{99}=\dfrac{594+46}{99}=\dfrac{640}{99}$

Multiply $4.28$ and $0.67.$ Round off the product obtained correct to three decimal places

  1. $2.798$

  2. $2.868$

  3. $0.85$

  4. None of these


Correct Option: B
Explanation:

$4.28 \times 0.67 = 2.8676$

As the digit in the fourth place $(6)$ is greater than $5,$ it will get rounded.
$\therefore  2.8676$  can be written as $2.868$, correct to three decimal places.

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