To solve these problems, we need to multiply the decimal number by the power of 10.
The Rule:
When you multiply a number by $10^n$ (where $n$ is the exponent), you move the decimal point to the
right by $n$ places.
* If you run out of digits, add zeros.
* If the exponent is negative (not in this worksheet), you would move left. Here, all exponents are positive.
Let's go through each problem step-by-step:
1.
$.8 \times 10^2$
* Exponent is 2, so move the decimal point 2 places to the right.
* $.8 \rightarrow 8. \rightarrow 80.$
* Answer:
80
2.
$.67 \times 10^3$
* Exponent is 3, so move the decimal point 3 places to the right.
* $.67 \rightarrow 6.7 \rightarrow 67. \rightarrow 670.$
* Answer:
670
3.
$1.24 \times 10^3$
* Exponent is 3, so move the decimal point 3 places to the right.
* $1.24 \rightarrow 12.4 \rightarrow 124. \rightarrow 1240.$
* Answer:
1,240
4.
$300.2 \times 10^2$
* Exponent is 2, so move the decimal point 2 places to the right.
* $300.2 \rightarrow 3002. \rightarrow 30020.$
* Answer:
30,020
5.
$.6 \times 10^2$
* Exponent is 2, so move the decimal point 2 places to the right.
* $.6 \rightarrow 6. \rightarrow 60.$
* Answer:
60
6.
$9.61 \times 10^6$
* Exponent is 6, so move the decimal point 6 places to the right.
* Current digits after decimal: 6 and 1 (2 digits). We need to move 6 places total.
* Move past 6 and 1 (2 moves): $961.$
* Need 4 more moves, so add four zeros: $9610000.$
* Answer:
9,610,000
7.
$.89 \times 10^4$
* Exponent is 4, so move the decimal point 4 places to the right.
* $.89 \rightarrow 8.9 \rightarrow 89. \rightarrow 890. \rightarrow 8900.$
* Answer:
8,900
8.
$80.6 \times 10^4$
* Exponent is 4, so move the decimal point 4 places to the right.
* $80.6 \rightarrow 806. \rightarrow 8060. \rightarrow 80600. \rightarrow 806000.$
* Answer:
806,000
9.
$13.7 \times 10^2$
* Exponent is 2, so move the decimal point 2 places to the right.
* $13.7 \rightarrow 137. \rightarrow 1370.$
* Answer:
1,370
10.
$.54 \times 10^2$
* Exponent is 2, so move the decimal point 2 places to the right.
* $.54 \rightarrow 5.4 \rightarrow 54.$
* Answer:
54
11.
$20.8 \times 10^4$
* Exponent is 4, so move the decimal point 4 places to the right.
* $20.8 \rightarrow 208. \rightarrow 2080. \rightarrow 20800. \rightarrow 208000.$
* Answer:
208,000
12.
$12.89 \times 10^1$
* Exponent is 1, so move the decimal point 1 place to the right.
* $12.89 \rightarrow 128.9$
* Answer:
128.9
──────────────────────────────────────
Final Answer:
.8 x 10² = 80
.67 x 10³ = 670
1.24 x 10³ = 1,240
300.2 x 10² = 30,020
.6 x 10² = 60
9.61 x 10⁶ = 9,610,000
.89 x 10⁴ = 8,900
80.6 x 10⁴ = 806,000
13.7 x 10² = 1,370
.54 x 10² = 54
20.8 x 10⁴ = 208,000
12.89 x 10¹ = 128.9
Parent Tip: Review the logic above to help your child master the concept of free worksheet for 8th graders.
