Here are the solutions to the problems on your worksheet.
Write the following in scientific notation:
1.
384.32
To write this in scientific notation, move the decimal point so there is only one non-zero digit to its left. Move the decimal 2 places to the left (from after the 4 to between the 3 and the 8). Since you moved it 2 places, the exponent is 2.
Answer: $3.8432 \times 10^2$
2.
87521
Move the decimal point 4 places to the left to get 8.7521. The exponent is 4.
Answer: $8.7521 \times 10^4$
3.
$3910.28 \times 10^4$
First, convert 3910.28 into proper scientific notation. Move the decimal 3 places to the left to get $3.91028 \times 10^3$.
Now combine the exponents: $(3.91028 \times 10^3) \times 10^4$.
Add the exponents together: $3 + 4 = 7$.
Answer: $3.91028 \times 10^7$
4.
0.001247
Move the decimal point 3 places to the right to get 1.247. Since the original number is small (less than 1), the exponent is negative.
Answer: $1.247 \times 10^{-3}$
Write the following in standard form:
5.
$3.23 \times 10^{-6}$
The negative exponent means the number is very small. Move the decimal point 6 places to the left. You will need to add zeros as placeholders.
Answer: $0.00000323$
6.
$1.589 \times 10^4$
The positive exponent means the number is large. Move the decimal point 4 places to the right. Add zeros for the empty spaces.
Answer: $15,890$
7.
$8.29 \times 10^1$
Move the decimal point 1 place to the right.
Answer: $82.9$
8.
$6.75 \times 10^{-3}$
Move the decimal point 3 places to the left. Add zeros as placeholders.
Answer: $0.00675$
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Final Answer:
1. $3.8432 \times 10^2$
2. $8.7521 \times 10^4$
3. $3.91028 \times 10^7$
4. $1.247 \times 10^{-3}$
5. $0.00000323$
6. $15,890$
7. $82.9$
8. $0.00675$
Parent Tip: Review the logic above to help your child master the concept of scientific notations worksheet.
