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Math  /  Numbers & Operations

Question1.6⋅10−5⋅1000mn1 m=1.6 \cdot 10^{-5} \cdot \frac{1000 \mathrm{mn}}{1 \mathrm{~m}}=

Studdy Solution

STEP 1

1. The expression 1.6⋅10−5⋅1000mn1 m1.6 \cdot 10^{-5} \cdot \frac{1000 \mathrm{mn}}{1 \mathrm{~m}} involves multiplication and division of numbers in scientific notation.
2. The units need to be handled appropriately, assuming mn\mathrm{mn} stands for millinewton and m\mathrm{m} stands for meter.
3. The goal is to simplify the given expression to a single numerical value with appropriate units.

STEP 2

1. Simplify the numerical part of the expression.
2. Simplify the units in the expression.
3. Combine the results from steps 1 and 2 to get the final simplified form.

STEP 3

Identify and simplify the numerical part of the expression:
1.6⋅10−5⋅10001.6 \cdot 10^{-5} \cdot 1000

STEP 4

Simplify the multiplication:
1.6⋅10−5⋅1000=1.6⋅10−5⋅1031.6 \cdot 10^{-5} \cdot 1000 = 1.6 \cdot 10^{-5} \cdot 10^3

STEP 5

Combine the powers of 10:
1.6⋅10−5+3=1.6⋅10−21.6 \cdot 10^{-5+3} = 1.6 \cdot 10^{-2}

STEP 6

Simplify the units. Recognize that mnm\frac{\mathrm{mn}}{\mathrm{m}} can be expressed with mn\mathrm{mn} representing millinewton (10−310^{-3} N):
1000mn1 m=1000⋅10−3Nm=1Nm\frac{1000 \mathrm{mn}}{1 \mathrm{~m}} = 1000 \cdot 10^{-3} \frac{\mathrm{N}}{\mathrm{m}} = 1 \frac{\mathrm{N}}{\mathrm{m}}

STEP 7

Combine the results from steps 1 and 2. The numerical part is 1.6⋅10−21.6 \cdot 10^{-2} and the unit part is Nm\frac{\mathrm{N}}{\mathrm{m}}:
1.6⋅10−2Nm=0.016Nm1.6 \cdot 10^{-2} \frac{\mathrm{N}}{\mathrm{m}} = 0.016 \frac{\mathrm{N}}{\mathrm{m}}
Solution:
1.6⋅10−5⋅1000mn1 m=0.016Nm1.6 \cdot 10^{-5} \cdot \frac{1000 \mathrm{mn}}{1 \mathrm{~m}} = 0.016 \frac{\mathrm{N}}{\mathrm{m}}

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