Answer :
Sure, let's match each decimal number to its equivalent in scientific notation step by step:
1. Step-by-Step Solution:
- Decimal: [tex]\( 0.015 \)[/tex]
- Scientific Notation: To convert [tex]\( 0.015 \)[/tex] to scientific notation, we move the decimal point two places to the right, which gives us [tex]\( 1.5 \)[/tex]. Therefore, the scientific notation is [tex]\( 1.5 \times 10^{-2} \)[/tex].
- Match: [tex]\( 1.5 \times 10^{-2} \rightarrow 0.015 \)[/tex]
- Decimal: [tex]\( 15 \)[/tex]
- Scientific Notation: To convert [tex]\( 15 \)[/tex] to scientific notation, we move the decimal point one place to the left, giving us [tex]\( 1.5 \)[/tex]. Therefore, the scientific notation is [tex]\( 1.5 \times 10^1 \)[/tex].
- Match: [tex]\( 1.5 \times 10^1 \rightarrow 15 \)[/tex]
- Decimal: [tex]\( 150 \)[/tex]
- Scientific Notation: To convert [tex]\( 150 \)[/tex] to scientific notation, we move the decimal point two places to the left, giving us [tex]\( 1.5 \)[/tex]. Therefore, the scientific notation is [tex]\( 1.5 \times 10^2 \)[/tex].
- Match: [tex]\( 1.5 \times 10^2 \rightarrow 150 \)[/tex]
- Decimal: [tex]\( 1.5 \)[/tex]
- Scientific Notation: To convert [tex]\( 1.5 \)[/tex] to scientific notation, the decimal point is already in the correct position, so it remains [tex]\( 1.5 \times 10^0 \)[/tex].
- Match: [tex]\( 1.5 \times 10^0 \rightarrow 1.5 \)[/tex]
- Decimal: [tex]\( 0.15 \)[/tex]
- Scientific Notation: To convert [tex]\( 0.15 \)[/tex] to scientific notation, we move the decimal point one place to the right, giving us [tex]\( 1.5 \)[/tex]. Therefore, the scientific notation is [tex]\( 1.5 \times 10^{-1} \)[/tex].
- Match: [tex]\( 1.5 \times 10^{-1} \rightarrow 0.15 \)[/tex]
2. Final Matches:
- [tex]\( 1.5 \times 10^{-2} \rightarrow 0.015 \)[/tex]
- [tex]\( 1.5 \times 10^1 \rightarrow 15 \)[/tex]
- [tex]\( 1.5 \times 10^2 \rightarrow 150 \)[/tex]
- [tex]\( 1.5 \times 10^0 \rightarrow 1.5 \)[/tex]
- [tex]\( 1.5 \times 10^{-1} \rightarrow 0.15 \)[/tex]
These are the correct matches of the decimal numbers to their respective equivalents in scientific notation.
1. Step-by-Step Solution:
- Decimal: [tex]\( 0.015 \)[/tex]
- Scientific Notation: To convert [tex]\( 0.015 \)[/tex] to scientific notation, we move the decimal point two places to the right, which gives us [tex]\( 1.5 \)[/tex]. Therefore, the scientific notation is [tex]\( 1.5 \times 10^{-2} \)[/tex].
- Match: [tex]\( 1.5 \times 10^{-2} \rightarrow 0.015 \)[/tex]
- Decimal: [tex]\( 15 \)[/tex]
- Scientific Notation: To convert [tex]\( 15 \)[/tex] to scientific notation, we move the decimal point one place to the left, giving us [tex]\( 1.5 \)[/tex]. Therefore, the scientific notation is [tex]\( 1.5 \times 10^1 \)[/tex].
- Match: [tex]\( 1.5 \times 10^1 \rightarrow 15 \)[/tex]
- Decimal: [tex]\( 150 \)[/tex]
- Scientific Notation: To convert [tex]\( 150 \)[/tex] to scientific notation, we move the decimal point two places to the left, giving us [tex]\( 1.5 \)[/tex]. Therefore, the scientific notation is [tex]\( 1.5 \times 10^2 \)[/tex].
- Match: [tex]\( 1.5 \times 10^2 \rightarrow 150 \)[/tex]
- Decimal: [tex]\( 1.5 \)[/tex]
- Scientific Notation: To convert [tex]\( 1.5 \)[/tex] to scientific notation, the decimal point is already in the correct position, so it remains [tex]\( 1.5 \times 10^0 \)[/tex].
- Match: [tex]\( 1.5 \times 10^0 \rightarrow 1.5 \)[/tex]
- Decimal: [tex]\( 0.15 \)[/tex]
- Scientific Notation: To convert [tex]\( 0.15 \)[/tex] to scientific notation, we move the decimal point one place to the right, giving us [tex]\( 1.5 \)[/tex]. Therefore, the scientific notation is [tex]\( 1.5 \times 10^{-1} \)[/tex].
- Match: [tex]\( 1.5 \times 10^{-1} \rightarrow 0.15 \)[/tex]
2. Final Matches:
- [tex]\( 1.5 \times 10^{-2} \rightarrow 0.015 \)[/tex]
- [tex]\( 1.5 \times 10^1 \rightarrow 15 \)[/tex]
- [tex]\( 1.5 \times 10^2 \rightarrow 150 \)[/tex]
- [tex]\( 1.5 \times 10^0 \rightarrow 1.5 \)[/tex]
- [tex]\( 1.5 \times 10^{-1} \rightarrow 0.15 \)[/tex]
These are the correct matches of the decimal numbers to their respective equivalents in scientific notation.
