We can estimate decimal division by rounding each decimal to the nearest whole number and dividing the resulting numbers.

For example, suppose we wish to estimate the quotient of the following division problem. 19.7 \div 5.3

One way to proceed is first to round both quantities to the nearest whole number:

\begin{array}{ccccl} 19.7 & \div & 5.3 \\ \big\downarrow && \big\downarrow \\ \color{blue}20 & \div & \color{blue}5 \end{array}

So, we can form an estimate of 19.7 \div 5.3 by evaluating 20 \div 5.

Computing the quotient of this simplified problem gives

20 \div 5 = 4.

Therefore, 19.7 \div 5.3 is approximately equal to 4. We can write this symbolically as follows: 19.7 \div 5.3 \approx 4

The symbol \approx means "is approximately equal to."

FLAG

By rounding the dividend to the nearest whole number, estimate the value of 94.8 \div 5.

EXPLANATION

First, we round the dividend to the nearest whole number: 94.8 \rightarrow 95

Hence, we need to find the value of 95 \div 5. Computing the quotient, we get:

1 9
5 \!\!\require{enclose}\enclose{longdiv}{9 {\:\phantom{|}} 5}
-\!\!\!\!\!\!\! 5
4 5
-\!\!\!\!\!\!\! 4 5
0

Hence, 95 \div 5 = 19.

Therefore, 94.8 \div 5 is approximately equal to 19.

FLAG

Estimate the value of $16.4 \div 3.6$ by rounding each number to the nearest whole number.

a
$4$
b
$5$
c
$3$
d
$2$
e
$1$

By rounding the dividend to the nearest whole number, estimate the value of $96.2 \div 4.$

a
$22$
b
$25$
c
$24$
d
$26$
e
$23$

Estimate 12.3 \div 106.8 by rounding the divisor to the nearest hundred.

EXPLANATION

First, we round the divisor to the nearest hundred: 106.8 \rightarrow 100

Now, we need to compute

12.3 \div 100.

There are two zeros in 100, so we move the decimal point two places to the left:

12.3 \rightarrow 0.123

Therefore, 12.3 \div 106.8 is approximately equal to 0.123 \, .

FLAG

Estimate $4.3 \div 11.1$ by rounding the divisor to the nearest ten.

a
$11.4$
b
$0.43$
c
$43$
d
$0.34$
e
$0.043$

Estimate $6.4 \div 97.7$ by rounding the divisor to the nearest hundred.

a
$6.4$
b
$64$
c
$0.064$
d
$0.64$
e
$9.77$

Estimate $1455 \div 990$ by rounding the divisor to the nearest thousand.

a
$14.55$
b
$0.1455$
c
$145.5$
d
$1450$
e
$1.455$

Estimate the value of 206.6 \div 3.43 by rounding each number to the nearest whole number.

EXPLANATION

We round both numbers to the nearest whole number: \begin{array}{ccccl} 206.6 & \div & 3.43 \\ \big\downarrow && \big\downarrow \\ \color{blue}207 & \div & \color{blue}3 \end{array}

Now, we need to find the value of

207 \div 3.

So, we go through the long division procedure as usual:

6 9
3 \!\!\require{enclose}\enclose{longdiv}{2 {\:\phantom{|}} 0 {\:\phantom{|}} 7}
-\!\!\!\! 1 8
2 7
-\!\!\!\! 2 7
\fbox{0}

Therefore, 206.6 \div 3.43 is approximately equal to 69.

FLAG

By rounding the divisor to the nearest whole number, estimate the value of $124 \div 4.15.$

a
$31$
b
$30$
c
$32$
d
$35$
e
$33$

Estimate the value of $374.5 \div 5.05$ by rounding each number to the nearest whole number. Round your final answer to the nearest whole number.

a
$77$
b
$89$
c
$73$
d
$75$
e
$71$

Estimate the value of 116.8 \div 5.15 by rounding each number to the nearest whole number. Round your final answer to the nearest whole number.

EXPLANATION

We round both numbers to the nearest whole number: \begin{array}{ccccl} 116.8 & \div & 5.15 \\ \big\downarrow && \big\downarrow \\ \color{blue}117 & \div & \color{blue}5 \end{array}

Now, we need to find the value of 117\div 5.

So, we go through the long division procedure as usual:

2 3
5 \!\!\require{enclose}\enclose{longdiv}{1 {\:\phantom{|}} 1 {\:\phantom{|}} 7}
-\!\!\!\!\!\!\! 1 0
1 7
-\!\!\!\!\! 1 5
\fbox{2}

Therefore, 117 \div 5 = 23\,\text{R}2.

The remainder 2 is closer to 0 than to the divisor 5. So, to round to the nearest whole number, we must round down:

117 \div 5 \rightarrow 23

Therefore, 116.8 \div 5.15 is approximately equal to 23.

FLAG

Estimate the value of $262.5 \div 3.09$ by rounding each number to the nearest whole number. Round your final answer to the nearest whole number.

a
$90$
b
$86$
c
$89$
d
$87$
e
$88$

Estimate the value of $284.9 \div 8.53$ by rounding each number to the nearest whole number. Round your final answer to the nearest whole number.

a
$32$
b
$34$
c
$33$
d
$35$
e
$31$
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