# How do you calculate the following retaining the correct number of significant figures 12.432 times 3= and 208 times 62.1 =

Question
Decimals
How do you calculate the following retaining the correct number of significant figures $$\displaystyle{12.432}\times{3}=$$ and $$\displaystyle{208}\times{62.1}=$$

2021-02-07
Step 1 Firstly we calculate the first part. Multiply both the numbers After that round off the result at tenth place. $$\displaystyle{12.432}\times{3}={37.296}$$
$$\displaystyle{37.396}\approx{37.4}$$ Step 2 Significant figures are those that have some meaning in overall value of the number. To determine what numbers are significant and which aren't, use the following rules: 1) Zero to the left of the decimal value less than 1 is not significant. 2) All trailing zeros are not significant. 3) Zeros between non zero numbers are significant. 4) All non zero numbers are significant. 5) If a number has more numbers than the desired numbers of significant digits, the number is rounded. For example, 532.500 is 533.000 to 3 significant digits. Step 3 So, here result is: Here 1 significant figure. Decimals: 0 $$\displaystyle{12.432}\times{3}$$
$$\displaystyle={37.296}$$
$$\displaystyle={40}$$ Step 4 Now come to the next part. So, total 3 significant figures. Decimals: 0 $$\displaystyle{208}\times{62.1}={12916.8}$$
$$\displaystyle{12916.8}\approx{12900}$$

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