Exercise 1.1 - Chapter 1 Number Systems Term 3 7th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

Ex $1.1$
Question 1.
Round each of the following decimals to the nearest whole number.
(i) $8.71$
(ii) $26.01$
(iii) $69.48$
(iv) $103.72$
(v) $49.84$
(vi) $101.35$
(vii) $39.814$
(viii) $1.23$
Solution.
(i) $8.71$
Underlining the digit to be rounded $\underline{8} .71$. Since the digit next to the underlined digit, 7 which is greater than 5 , adding 1 to the underlined digit.
Hence the nearest whole number $8.71$ rounds to is $\underline{9}$.
(ii) $26.01$
Underlining the digit to be rounded 2 $\underline{6} .01$. Since the digit next to the underlined digit, 0 which is less than 5 , the underlined digit 6 remains the same.
$\therefore$ The nearest whole number $26.01$ rounds to is 26 .
(iii) $69.48$
Underlining the digit to be rounded $69.48$. Since the digit next to the underlined digit, 4 which is less than 5 , the underlined digit 9 remains the same.
$\therefore$ The whole number is $69.48$ rounds to is 69 .
(iv) $103.72$
Underlining the digit to be rounded $10 \underline{3} .72$ since the digit next to the underlined digit, 7 which is greater than 5 , we add 1 to the under lined digit.
Hence the nearest whole number $103.72$ rounds to is 104 .
(v) $49.84$
Underlining the digit to be rounded $4 \underline{9} .84$. Since the digit next to the underlined digit 8 which is greater than 5, we add 1 to the underlined digit.
Hence the nearest whole number $49.84$ rounds to 50 .
(vi) $101.35$
Underlining the digit to be rounded $101.35$. Since the digit next to the underlined digit 3 is less than 5 , the underlined digit 1 remains the same.
Hence the nearest whole number $101.35$ rounds to is 101 .
(vii) $39.814$
Underlining the digit to be rounded $39.814$. Since the digit next to the underlined digit 8 is greater than 5 , we add 1 to the underlined digit.
Hence the nearest whole number $39.814$ rounds to is 40 .
(viii) $1.23$
Underlining the digit to be rounded $1.23$. Since the digit next to the underlined digit 2 , is less than 5 , the underlined digit 1 remains the same.
Hence the nearest whole number $1.23$ rounds to is 1 .

Question 2.
Round each decimal number to the given place value.
(i) $5.992$; tenths place
(ii) $21.805$; hundredth place
(iii) $35.0014$; thousandth place
Solution:
(i) 992 ; tenths place
Underlining the digit to be rounded 5.992. Since the digit next to the underlined digit is 9 greater than 5 , we add 1 to the underlined digit.
Hence the rounded number is $6.0$.
(ii) $21.805$; hundredth place
Underlining the digit to be rounded $21.805$ since the digit next to the underlined digit is 5 , we add 1 to the underlined digit.
Hence the rounded number is $21.81$.
(iii) $35.0014$; thousandth place
Underlining the digit to be rounded $35.00 \underline{14}$. Since the digit next to the underlined digit is 4 less
than 5 the underlined digit remains the same.
Hence the rounded number is $35.001$.

Question $3 .$
Round the following decimal numbers upto 1 places of decimal.
(i) $123.37$
(ii) $19.99$
(iii) $910.546$
Solution:
(i) $123.37$
Rounding $123.37$ upto one places of decimal means round to the nearest tenths place. Underling the digit in the tenths place of $123.37$ gives $123.37$. Since the digit next to the tenth place value is 7 which is greater than 5 , we add 1 to the underlined digit to get $123.4$. Hence the rounded value of $123.37$ upto one places of decimal is 123.4.
(ii) $19.99$
Rounding $19.99$ upto one places of decimal means round to the nearest tenth place. Underling the digit in the tenths place of $19.99$ gives 19. 99 . Since the digit next to the tenth place value is 9 which is greater than 5 , we add 1 to the underlined digit to get 20 .
Hence the rounded value of $19.99$ upto one places of decimal is $20.0$.
(iii) $910.546$
Rounding $910.546$ upto one places of decimal means round to the nearest tenths place underlining the digit in the tenths place of $910.546$ gives $910.546$. Since the digit next to the tenth place value is 4 , which is less than 5 the underlined digit remains the same. Hence the rounded value of $910.546$ upto one places of decimal is $910.5$.
 

Question $4 .$
Round the following decimal numbers upto 2 places of decimal.
(i) $87.755$
(ii) $301.513$
(iii) $79.997$
Solution:

(i) $87.755$
Rounding $87.755$ upto 2 places of decimal means round to the nearest hundredths place.
Underlining the digit in the hundredth place of $87.755$ gives $87.755$. Since the digit next to the hundredth place value is 5 , we add 1 to the underlined digit.
Hence the rounded value of $87.755$ upto two places of decimal is $87.76$.
(ii) $301.513$
Rounding $301.51$ upto 2 places of decimal means round to the nearest hundredths place.
Underlining the digit in the hundredth place of $301.513$ gives $301.5 \underline{13}$. Since the digit next to the underlined digit 3 is less than 5 , the underlined digit remains the same.
$\therefore$ The rounded value of $301.513$ upto 2 places of decimal is $301.51$.
(iii) $79.997$
Rounding $79.997$ upto 2 places of decimal means round to the nearest hundredths place.
Underlining the digit in the hundredth place of $79.997$ gives $79.997$. Since the digit next to the underlined digit 7 is greater than 5 , we add 1 to the underlined number.
Hence the rounded value of $79.997$ upto 2 places of decimal is $80.00$.

Question $5 .$
Round the following decimal numbers upto 3 place of decimal
(a) $24.4003$
(b) $1251.2345$
(c) $61.00203$
Solution:
(a) $24.4003$
Rounding $24.4003$ upto 3 places of decimal means rounding to the nearest thousandths place.
Underlining the digit in the thousandths place of $24.4003$ gives $24.40 \underline{0} 3$. In $24.40 \underline{0} 3$ the digit next to the thousandths value is 3 which is less than 5 .
$\therefore$ The underlined digit remains the same. So the rounded value of $24.4003$ upto 3 places of decimal is $24.400$.
(b) $1251.2345$
Rounding $1251.2345$ upto 3 places of decimal means rounding to the nearest thousandths place. Underlining the digit in the thousandths place of $1251.2345$ gives $1251.23 \underline{4}$, the digit next to the thousandths place value is 5 and so we add 1 to the underlined digit. So the rounded value of $1251.2345$ upto 3 places of decimal is $1251.235$.
(c) $61.00203$
Rounding $61.00203$ upto 3 places of decimal means rounding to the nearest thousandths place. Underlining the digit in the thousandth place of $61.00 \underline{2} 03$ gives $61.00 \underline{2} 03$. In $61.00203$, the digit next to the thousandths place value is 0 , which is less than 5 .

Hence the underlined digit remains the same. So the rounded value of $61.00203$ upto 3 places of decimal is $61.002$.