계산에서 자연수의 끝자리 0의 유효숫자 처리

계산에서 자연수의 끝자리 0의 유효숫자 처리

 

 

[계산에서 자연수의 끝자리 0의 유효숫자 처리]

 

(숫자 자체로만 판단하면, 자연수의 끝자리 0은 유효숫자가 아니지만,)

유효숫자 계산과 관련된 외국 사이트의 자료들을 정리해보면,

덧셈/뺄셈에서는 유효숫자에 포함시키고

곱셈/나눗셈에서는 유효숫자에 포함시키지 않고 있습니다.

( 덧셈/뺄셈에서는 유효숫자 자리 수에 포함시키고
곱셈/나눗셈에서는 유효숫자 개수에 포함시키지 않고 있습니다. )

 

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530 + 1.352 = 531.352

Answer: 531 ... 1의 자리에 맞춤

 

20 + 11.7 = 31.7

Answer: 32 ... 1의 자리에 맞춤

 

361 + 5200 = 5561

Answer: 5561 ... 1의 자리에 맞춤

 

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530 × 1.352 = 716.560

Answer: 720 ... 유효숫자 2개에 맞춤

 

20 × 11.7 = 234.0

Answer: 200 ... 유효숫자 1개에 맞춤

 

361 × 5200 = 1877200

Answer: 1900000 ... 유효숫자 2개에 맞춤

 

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[Rules for deciding the number of significant figures in a measured quantity]

 

▶ All non-zero digits are significant.

Ex. 5.4789

- All digits of are non-zero. Therefore, all digits are significant. Thus, it has 5 significant digits.

 

▶ Zeros located between non-zero digits are significant.

Ex. 2.00008

- All zeroes in this number are significant. Therefore, it has 6 significant digits.

 

▶ Zeros at the end of a number are significant if the number contains a decimal.

Ex. 45.00

- The zeros in this number are significant. Therefore, it has 4 significant digits.

 

▶ Zeros at the end of a number are significant if a decimal point is in place.

Ex. 12000.

- The zeros in this number are significant. Therefore, it has 5 significant digits.

 

▶ Zeros at the end of a number are insignificant if the number does not contain a decimal point.

Ex. 3400

- There zeros in this number are not significant. Therefore, it has 2 significant digits.

 

▶ Zeros to the left of the first non-zero digit after a decimal point are not significant.

Ex. 0.000076

- The zeros in this number are not significant. Therefore, it has 2 significant digits.

 

▶ The zeros after the first non-zero digit after a decimal point are significant.

Ex. 0.0005600

- The first 3 zeros are not significant. The last 2 zeros are. Therefore, this number has 4 significant digits.

 

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[Zero Type: trailing zeros in a whole number]

 

200 is considered to have only ONE significant figure while 25,000 has two.

 

This is based on the way each number is written. When whole number are written as above, the zeros, BY DEFINITION, did not require a measurement decision, thus they are not significant.

 

However, it is entirely possible that 200 really does have two or three significant figures. If it does, it will be written in a different manner than 200.

 

Typically, scientific notation is used for this purpose. If 200 has two significant figures, then 2.0×10^2 is used. If it has three, then 2.00×10^2 is used.

 

 

 

[ 관련 글 https://ywpop.tistory.com/10839 ] 자연수에서 유효 숫자 오른쪽에 있는 0.

 

 

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