Video: Studying Units of Weight and Conversion

What is 2.87 Γ— 10⁷ dynes in newtons?

02:35

Video Transcript

What is 2.87 multiplied by 10 to the power of seven dynes in newtons?

In order to answer this question, we need to recall the conversion between the two units. One newton is equal to 100,000 dynes. We know that 100,000 is equal to 10 to the power of five. This means that one newton is equal to 10 to the power of five dynes. To convert from newtons to dynes, we therefore multiply by 10 to the power of five. To convert from dynes to newtons, we divide by 10 to the power of five.

In this question, we want to convert 2.87 multiplied by 10 to the power of seven dynes into newtons. We therefore need to divide 2.87 multiplied by 10 to the power of seven by 10 to the power of five. At this stage, it is worth recalling one of our laws of indices or exponents. π‘₯ to the power of π‘Ž divided by π‘₯ to the power of 𝑏 is equal to π‘₯ to the power of π‘Ž minus 𝑏. When dividing, we can subtract the exponents. This means that 10 to the power of seven divided by 10 to the power of five is equal to 10 to the power of two, or 10 squared, as seven minus five equals two.

We’re therefore left with 2.87 multiplied by 10 squared. We could multiply 2.87 by 10 and then 10 again. However, as 10 squared is equal to 100, we can multiply 2.87 by 100. Multiplying by 100 moves all our digits two places to the left. This means that 2.87 multiplied by 10 to the power of seven dynes is 287 newtons.

An alternative method would have been to have written 2.87 multiplied by 10 to the power of seven as an ordinary number. We could then divide this by 100,000. This would also have given us an answer of 287 newtons.

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