Question

Which of these will give 109.86 after estimation to the nearest hundredths.

• A. 109.852
• B. 109.855
• C. 109.861
• D. 109.867

Answer 1

Answer: (B), (C)

109.861

Let's analyse each options.

For option A.

T	H	O	.	t	h	th
1	0	9	.	8	5	2

Digit in hundredths place = 5
Digit nearest to the hundredths place (right of it) = 2 (in thousandths place)

Rule for estimation: 2 (in thousandths place) nearest to hundredths is less than 5, so leave a digit in the hundredths place as it is.

Hence, 109. 852 becomes 109.85

For option B

T	H	O	.	t	h	th
1	0	9	.	8	5	5

Digit in hundredths place = 5
Digit nearest to the hundredths place (right of it) = 5 (in thousandths place)

Rule for estimation: 5 (in thousandths place) nearest to hundredths is equal to 5, so we increase the digit in the hundredths column by 1

$\Rightarrow 109.8\underset{–}{5}5\to 109.8\underset{–}{6}5$

Finally, we eliminate the digits after the rounded-off digits

Hence, 109.855 estimated to nearest hundredths is 109.86

For option C

T	H	O	.	t	h	th
1	0	9	.	8	6	1

Digit in hundredths place = 6
Digit nearest to the hundredths place (right of it) = 1 (in thousandths place)

Rule for estimation: 1 (in thousandths place) nearest to hundredths is less than 5, so leave a digit in the hundredths place as it is.

Hence, 109. 861 becomes 109.86

For option D

T	H	O	.	t	h	th
1	0	9	.	8	6	7

Digit in hundredths place = 6
Digit nearest to the hundredths place (right of it) = 7 (in thousandths place)

Rule for estimation: 7 (in thousandths place) nearest to hundredths is equal to 5, so we increase the digit in the hundredths column by 1

$\Rightarrow 109.8\underset{–}{6}7\to 109.8\underset{–}{7}7$

Finally, we eliminate the digits after the rounded-off digits

Hence, 109.877 estimated to nearest hundredths is 109.87

$\therefore$ Only option B and C are correct