Exercise 1.1 (Rounding of Decimals)

Exercise 1.1

1. Round each of the following decimals to the nearest whole number.

(i) 8.71

Underlining the digit to be rounded 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 9.

(ii) 26.01

Underlining the digit to be rounded 26.01. Since the digit next to the underlined digit, 0 which is less than 5, the underlined digit 6 remains the same.

∴ 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.

∴ The whole number is 69.48 rounds to is 69.

(iv) 103.72

Underlining the digit to be rounded 103.72 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 49.84. 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.

2. Round each decimal number to the given place value.

(i) 5.992 to tenth 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 to hundredth place

Underlining the digit to be rounded 21.805 since the digit next to the underlined digit is 5, we add I to the underlined digit. Hence the rounded number is 21.81.

(iii) 35.0014 to thousandth place

Underlining the digit to be rounded 35.0014. 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.

3. Round the following decimal numbers upto 1 places of decimal

(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.

4. Round the following decimal numbers upto 2 places of decimal

(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 301.513. Since the digit next to the underlined digit 3 is less than 5, the underlined digit remains the same.

∴ 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.

5. Round the following decimal numbers upto 3 place of decimal

(i) 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 24.4003. In 24.4003 the digit next to the thousandths value is 3 which is less than 5.

∴ The underlined digit remains the same. So the rounded value of 24.4003 upto 3 places of decimal is 24.400.

(ii) 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 1251.2345, 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.

(iii) 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 61.00203 gives 61.00203. 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.

ANSWERS:

Exercise 1.1

1. (i) 9 (ii) 26 (iii) 69 (iv) 104 (v) 50 (vi) 101 (vii) 40 (viii) 1

2. (i) 6.0 (ii) 21.81 (iii) 35.001

3. (i) 123.4 (ii) 20.0 (iii) 910.6

4. (i) 87.76 (ii) 301.51 (iii) 80.00

5. (i) 24.400 (ii) 1251.235 (iii) 61.002