To convert a number from scientific notation to decimal form, you look at the exponent (the small number) on the 10.
* If the exponent is
positive, move the decimal point to the
right.
* The number tells you exactly how many spaces to jump.
* If you run out of numbers, fill the empty spaces with zeros.
Here is the step-by-step solution for each problem:
1. $7.23 \times 10^4$
The exponent is 4, so move the decimal 4 spots to the right.
Start: $7.23$
Move 1: $72.3$
Move 2: $723.$
Move 3: $7230$ (add a zero)
Move 4: $72300$ (add another zero)
Result:
72,300
2. $8.12 \times 10^{-3}$
The exponent is -3, so move the decimal 3 spots to the
left.
Start: $8.12$
Move 1: $.812$
Move 2: $.0812$ (add a zero)
Move 3: $.00812$ (add another zero)
Result:
0.00812
3. $4.521 \times 10^1$
The exponent is 1, so move the decimal 1 spot to the right.
Start: $4.521$
Move 1: $45.21$
Result:
45.21
4. $6.124 \times 10^7$
The exponent is 7, so move the decimal 7 spots to the right.
Start: $6.124$
We have 3 digits after the decimal ($1, 2, 4$). We need to move 7 spots total.
$7 - 3 = 4$. So we move past the existing numbers and add 4 zeros.
$6,124$ followed by $0000$.
Result:
61,240,000
5. $8.47 \times 10^2$
The exponent is 2, so move the decimal 2 spots to the right.
Start: $8.47$
Move 1: $84.7$
Move 2: $847.$
Result:
847
6. $9.563 \times 10^5$
The exponent is 5, so move the decimal 5 spots to the right.
Start: $9.563$
We have 3 digits after the decimal. We need 5 moves.
$5 - 3 = 2$. Add 2 zeros to the end.
$9563$ followed by $00$.
Result:
956,300
7. $1.25 \times 10^8$
The exponent is 8, so move the decimal 8 spots to the right.
Start: $1.25$
We have 2 digits after the decimal. We need 8 moves.
$8 - 2 = 6$. Add 6 zeros to the end.
$125$ followed by $000000$.
Result:
125,000,000
8. $6.333 \times 10^4$
The exponent is 4, so move the decimal 4 spots to the right.
Start: $6.333$
We have 3 digits after the decimal. We need 4 moves.
$4 - 3 = 1$. Add 1 zero to the end.
$6333$ followed by $0$.
Result:
63,330
9. $4.56 \times 10^4$
The exponent is 4, so move the decimal 4 spots to the right.
Start: $4.56$
We have 2 digits after the decimal. We need 4 moves.
$4 - 2 = 2$. Add 2 zeros to the end.
$456$ followed by $00$.
Result:
45,600
10. $8.457 \times 10^3$
The exponent is 3, so move the decimal 3 spots to the right.
Start: $8.457$
Move 1: $84.57$
Move 2: $845.7$
Move 3: $8457.$
Result:
8,457
Final Answer:
1. 72,300
2. 0.00812
3. 45.21
4. 61,240,000
5. 847
6. 956,300
7. 125,000,000
8. 63,330
9. 45,600
10. 8,457
Parent Tip: Review the logic above to help your child master the concept of grade 8 math worksheet.
