Problem Analysis:
The worksheet provided is about metric conversions, specifically focusing on how to convert between different metric prefixes. The key concepts involve understanding the relationship between prefixes (e.g., kilo-, centi-, milli-) and their corresponding numerical values (powers of 10). The examples given illustrate how to move the decimal point based on the difference in steps between two prefixes.
Solution Explanation:
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Step 1: Understand the Metric Prefix Table
The table shows the relationship between metric prefixes and their numerical values:
-
Going up the table (left): Move the decimal point to the left.
-
Going down the table (right): Move the decimal point to the right.
- Each step represents a factor of 10 (e.g., kilo- to hecto- is one step, which means multiplying or dividing by 10).
####
Step 2: Analyze the Examples
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Example 1: Convert 1.0 kg to mg
1.
Identify the prefixes involved:
-
Kilo- (k): \(10^3\)
-
Milli- (m): \(10^{-3}\)
2.
Determine the difference in steps:
- From kilo- to milli- involves moving through the following steps: kilo → hecto → deka → NO PREFIX → deci → centi → milli.
- This is a total of
6 steps.
3.
Move the decimal point:
- Since we are converting from a larger unit (kg) to a smaller unit (mg), we move the decimal point
6 places to the right.
- \(1.0 \, \text{kg} = 1,000,000 \, \text{mg}\).
4.
Verification:
- \(1 \, \text{kg} = 10^3 \, \text{g}\).
- \(1 \, \text{g} = 10^3 \, \text{mg}\).
- Therefore, \(1 \, \text{kg} = 10^3 \times 10^3 = 10^6 \, \text{mg}\).
- This confirms that \(1.0 \, \text{kg} = 1,000,000 \, \text{mg}\).
#####
Example 2: Convert 2.3 cm to m
1.
Identify the prefixes involved:
-
Centi- (c): \(10^{-2}\)
-
No prefix (unit) for meters: \(10^0\)
2.
Determine the difference in steps:
- From centi- to no prefix involves moving through the following steps: centi → deci → NO PREFIX.
- This is a total of
2 steps.
3.
Move the decimal point:
- Since we are converting from a smaller unit (cm) to a larger unit (m), we move the decimal point
2 places to the left.
- \(2.3 \, \text{cm} = 0.023 \, \text{m}\).
4.
Verification:
- \(1 \, \text{cm} = 10^{-2} \, \text{m}\).
- Therefore, \(2.3 \, \text{cm} = 2.3 \times 10^{-2} = 0.023 \, \text{m}\).
- This confirms that \(2.3 \, \text{cm} = 0.023 \, \text{m}\).
Final Answer:
\[
\boxed{1,000,000 \, \text{mg} \quad \text{and} \quad 0.023 \, \text{m}}
\]
Parent Tip: Review the logic above to help your child master the concept of metric conversion worksheet answer key.
