ROUNDING NUMBERS WITH SIGNIFICANT FIGURES

Problem 1 :

a)  3.642 correct to 2 significant figures

b)  314269 correct to 3 significant figures

c)  0.00723 correct to 1 significant figure

Solution :

a)  3.642 correct to 2 significant figures

• Underline the second digit,

3.642

• The 3rd digit is 4, lesser than 5.

3.6

• Leaving the digit as it is.

So, the answer is 3.6.

b)  314269 correct to 3 significant figures

• Underline the second digit,

314269

• The 4^th digit is 2, lesser than 5.

314

• Leaving the digit as it is.

So, the answer is 314.

c)  0.00723 correct to 1 significant figure

• Rounding 1 significant figure is rounding for integer.
• Underline the first nonzero digit.

0.00723

• Since it is 7 (greater than 5), then it is 1

So, the answer is 1.

Problem 2 :

Correct the following decimal to 2 significant figures

Solution :

a)  1.473 correct to 2 significant figures

• Underline the second digit,

1.473

• The 3rd digit is 7, lesser than 5.
• Adding 1 with the underlined digit, then 1.5
• Answer is 1.5

b)  6.254 correct to 2 significant figures

• Underline the second digit,

6.254

• The 3rd digit is 5, it is equal to 5.
• Adding 1 with the underlined digit, then 6.3
• Answer is 6.3

c)  3.216 correct to 2 significant figures

• Underline the second digit,

3.216

• The 3^rd digit is 1, it is lesser than 5.
• Leave the digit as it is.
• Answer is 3.2

d)  10.68 correct to 2 significant figures

• Underline the second digit,

10.68

• The 3^rd digit is 6, it is greater than 5.
• Add 1 with the underlined digit.
• Answer is 11

e)  142 correct to 2 significant figures

• Underline the second digit,

142

• The 3^rd digit is 2, it is lesser than or equal to 5
• No change in the underlined digit.
• Answer is 14.

f)  1374 correct to 2 significant figures

• Underline the second digit,

1374

• The 3^rd digit is 7, it is greater than 5
• Add 1 with the underlined digit.
• Answer is 14.

Problem 3 :

Write the number 147.52 correct to.

a)  4 significant figures

b)  3 significant figures

c)  2 significant figures

Solution :

147.52

a) Rounding for 4 significant figures :

• Underline the 4th digit.

147.52

• Look at the 5th digit, it is 2 (lesser than 5)
• There is no change in the underlined digit.
• So, the answer is 147.5

b) Rounding for 3 significant figures :

• Underline the 3rd digit.

147.52

• Look at the 4th digit , it is 5 (equal to 5)
• Add 1 with the underlined digit.
• So, the answer is 148.

c) Rounding for 2 significant figures :

• Underline the 2nd digit.

147.52

• Look at the 3rd digit , it is 7 (greater than 5)
• Add 1 with the underlined digit.
• So, the answer is 15.

Problem 4 :

Write each of the numbers below to 3 significant figures.

Solution :

a)  18.47

• Underline the 3^rd digit.

18.47

• Look at the 4th digit , it is 7 (greater than 5)
• Add 1 with the underlined digit.
• So, the answer is 18.5

b)  0.003265

• Underline the 3^rd digit.

0.003265

• Look at the 4th digit , it is 2 (lesser than 5)
• No change in the underlined digit.
• So, the answer is 0.003

c) 147300

• Underline the 3^rd digit.

147300

• Look at the 4th digit , it is 3 (lesser than 5)
• No change in the underlined digit.
• So, the answer is 147.

d)  62.999

• Underline the 3^rd digit.

62.999

• Look at the 4th digit , it is 9 (greater than 5)
• Adding 1 with the underlined digit, we get 63
• So, the answer is 63.

e)  0.036247

• Underline the 3^rd digit.

0.036247

• Look at the 4th digit , it is 2 (lesser than 5)
• No change in the underlined digit
• So, the answer is 0.036

f)  0.00036945

• Underline the 3^rd digit.

0.00036945

• Look at the 4th digit , it is 3 (lesser than 5)
• No change in the underlined digit
• So, the answer is 0.