Problem:
The task is to convert the given numbers in
scientific notation into their
decimal form. The numbers are provided in scientific notation, and we need to write them out in decimal format.
#### Scientific Notation Recap:
Scientific notation is a way of expressing very large or very small numbers in the form:
\[
a \times 10^n
\]
where:
- \( a \) is a number between 1 and 10 (inclusive of 1 but exclusive of 10),
- \( n \) is an integer (positive or negative).
To convert from scientific notation to decimal form:
- If \( n \) is positive, move the decimal point \( n \) places to the
right.
- If \( n \) is negative, move the decimal point \( |n| \) places to the
left.
#### Given Numbers:
1. \( 7.23 \times 10^4 \)
2. \( 8.12 \times 10^{-3} \)
3. \( 4.521 \times 10^1 \)
4. \( 6.124 \times 10^7 \)
5. \( 8.47 \times 10^2 \)
6. \( 9.563 \times 10^5 \)
7. \( 1.25 \times 10^1 \)
8. \( 6.333 \times 10^6 \)
9. \( 4.56 \times 10^1 \)
10. \( 8.457 \times 10^2 \)
#### Solution:
1.
\( 7.23 \times 10^4 \):
- \( n = 4 \) (positive), so move the decimal point 4 places to the right.
- \( 7.23 \rightarrow 72300 \).
-
Decimal Form: \( 72300 \).
2.
\( 8.12 \times 10^{-3} \):
- \( n = -3 \) (negative), so move the decimal point 3 places to the left.
- \( 8.12 \rightarrow 0.00812 \).
-
Decimal Form: \( 0.00812 \).
3.
\( 4.521 \times 10^1 \):
- \( n = 1 \) (positive), so move the decimal point 1 place to the right.
- \( 4.521 \rightarrow 45.21 \).
-
Decimal Form: \( 45.21 \).
4.
\( 6.124 \times 10^7 \):
- \( n = 7 \) (positive), so move the decimal point 7 places to the right.
- \( 6.124 \rightarrow 61240000 \).
-
Decimal Form: \( 61240000 \).
5.
\( 8.47 \times 10^2 \):
- \( n = 2 \) (positive), so move the decimal point 2 places to the right.
- \( 8.47 \rightarrow 847 \).
-
Decimal Form: \( 847 \).
6.
\( 9.563 \times 10^5 \):
- \( n = 5 \) (positive), so move the decimal point 5 places to the right.
- \( 9.563 \rightarrow 956300 \).
-
Decimal Form: \( 956300 \).
7.
\( 1.25 \times 10^1 \):
- \( n = 1 \) (positive), so move the decimal point 1 place to the right.
- \( 1.25 \rightarrow 12.5 \).
-
Decimal Form: \( 12.5 \).
8.
\( 6.333 \times 10^6 \):
- \( n = 6 \) (positive), so move the decimal point 6 places to the right.
- \( 6.333 \rightarrow 6333000 \).
-
Decimal Form: \( 6333000 \).
9.
\( 4.56 \times 10^1 \):
- \( n = 1 \) (positive), so move the decimal point 1 place to the right.
- \( 4.56 \rightarrow 45.6 \).
-
Decimal Form: \( 45.6 \).
10.
\( 8.457 \times 10^2 \):
- \( n = 2 \) (positive), so move the decimal point 2 places to the right.
- \( 8.457 \rightarrow 845.7 \).
-
Decimal Form: \( 845.7 \).
Final Answer:
\[
\boxed{
\begin{aligned}
1. & \ 72300 \\
2. & \ 0.00812 \\
3. & \ 45.21 \\
4. & \ 61240000 \\
5. & \ 847 \\
6. & \ 956300 \\
7. & \ 12.5 \\
8. & \ 6333000 \\
9. & \ 45.6 \\
10. & \ 845.7
\end{aligned}
}
\]
Parent Tip: Review the logic above to help your child master the concept of mathematics worksheet for grade 8.
