To convert numbers from scientific notation to standard notation, we look at the exponent of 10.
* If the exponent is
positive, move the decimal point to the
right.
* If the exponent is
negative, move the decimal point to the
left.
Here is the step-by-step solution for each problem:
1)
$1.89 \times 10^4$
The exponent is 4 (positive). Move the decimal 4 places to the right.
$1.89 \rightarrow 18.9 \rightarrow 189 \rightarrow 1,890 \rightarrow 18,900$
Answer:
18,900
2)
$5.62 \times 10^{-3}$
The exponent is -3 (negative). Move the decimal 3 places to the left. We need to add zeros as placeholders.
$5.62 \rightarrow 0.562 \rightarrow 0.0562 \rightarrow 0.00562$
Answer:
0.00562
3)
$9.0812 \times 10^6$
The exponent is 6 (positive). Move the decimal 6 places to the right. Add zeros for the empty spots.
$9.0812 \rightarrow 908,120 \rightarrow 9,081,200$
Answer:
9,081,200
4)
$6.89 \times 10^{-4}$
The exponent is -4 (negative). Move the decimal 4 places to the left.
$6.89 \rightarrow 0.689 \rightarrow 0.0689 \rightarrow 0.00689 \rightarrow 0.000689$
Answer:
0.000689
5)
$2.913 \times 10^8$
The exponent is 8 (positive). Move the decimal 8 places to the right.
$2.913 \rightarrow 291,300,000$
Answer:
291,300,000
6)
$9.42 \times 10^{-6}$
The exponent is -6 (negative). Move the decimal 6 places to the left.
Count 6 spots left from after the 9: $0.00000942$
Answer:
0.00000942
7)
$4.039 \times 10^{-2}$
The exponent is -2 (negative). Move the decimal 2 places to the left.
$4.039 \rightarrow 0.4039 \rightarrow 0.04039$
Answer:
0.04039
8)
$7.13 \times 10^{-5}$
The exponent is -5 (negative). Move the decimal 5 places to the left.
Count 5 spots left from after the 7: $0.0000713$
Answer:
0.0000713
9)
$2.752 \times 10^{-9}$
The exponent is -9 (negative). Move the decimal 9 places to the left.
Count 9 spots left from after the 2: $0.000000002752$
Answer:
0.000000002752
10)
$8.4 \times 10^9$
The exponent is 9 (positive). Move the decimal 9 places to the right.
$8.4 \rightarrow 8,400,000,000$
Answer:
8,400,000,000
Final Answer:
1) 18,900
2) 0.00562
3) 9,081,200
4) 0.000689
5) 291,300,000
6) 0.00000942
7) 0.04039
8) 0.0000713
9) 0.000000002752
10) 8,400,000,000
Parent Tip: Review the logic above to help your child master the concept of introducing scientific notation worksheet 7th grade.
