Question

how many significant figures: 100.000 cl

Explanation:

Step1: Recall significant figure rules

For a number with a decimal point, all digits from the first non - zero digit to the end are significant. In the number \(100.000\), the first non - zero digit is \(1\), and then we have the zeros after the decimal point and the non - zero digit before. Let's count the digits: \(1\), \(0\), \(0\), \(0\), \(0\), \(0\)? Wait, no. Wait, \(100.000\) has digits: the \(1\), then three zeros before the decimal? No, wait, \(100.000\) is written as \(1\) followed by two zeros, then a decimal point, then three zeros. Wait, no, the number is \(100.000\). Let's break it down: the digits are \(1\), \(0\), \(0\), \(0\), \(0\), \(0\)? No, no. Wait, significant figure rules:
- Non - zero digits are significant.
- Zeros between non - zero digits are significant.
- Zeros after the decimal point (to the right of the decimal) are significant if there is a non - zero digit before the decimal.
- Leading zeros (zeros before the first non - zero digit) are not significant.

In \(100.000\), the first non - zero digit is \(1\). Then, the zeros after the decimal point (the three zeros) are significant, and the zeros between \(1\) and the decimal? Wait, no, \(100.000\) is \(1\times10^{2}+0\times10^{1}+0\times10^{0}+0\times10^{- 1}+0\times10^{-2}+0\times10^{-3}\). Wait, actually, when a number has a decimal point, all the digits from the first non - zero digit to the last digit (including zeros after the decimal) are significant. So in \(100.000\), the digits are \(1\), \(0\), \(0\), \(0\), \(0\), \(0\)? No, wait, no. Wait, \(100.000\) has six digits: \(1\), \(0\), \(0\), \(0\), \(0\), \(0\)? No, that's not right. Wait, \(100.000\) is \(1\) followed by two zeros, then a decimal, then three zeros. Wait, the correct way: the number \(100.000\) has the following significant figures: the \(1\), and then the five zeros? No, no. Wait, let's use the rule for numbers with decimals: all digits to the right of the first non - zero digit are significant, including zeros after the decimal. Wait, the number is \(100.000\). The first non - zero digit is \(1\). Then, the zeros after the decimal (the three zeros) are significant, and the zeros between \(1\) and the decimal? Wait, no, the zeros between \(1\) and the decimal: in \(100.000\), the digits are \(1\), \(0\), \(0\), \(0\), \(0\), \(0\)? No, I think I made a mistake. Let's count again. The number is \(100.000\). Let's write it as digits: position 1: \(1\), position 2: \(0\), position 3: \(0\), position 4: \(0\) (decimal point here? No, decimal point is after the third digit. So \(100.\) then \(000\). So the digits are \(1\), \(0\), \(0\), \(0\), \(0\), \(0\)? No, the decimal point is after the third digit, so the number is \(1\times10^{2}+0\times10^{1}+0\times10^{0}+0\times10^{-1}+0\times10^{-2}+0\times10^{-3}\). So the significant figures: the \(1\) is significant. The zeros after the decimal (the three zeros) are significant because there is a decimal point. Also, the zeros between \(1\) and the decimal: wait, no, in a number like \(100\), without a decimal, the trailing zeros are not significant (only \(1\) significant figure). But with a decimal, like \(100.\), it has three significant figures. But in \(100.000\), we have a decimal and three zeros after the decimal. So the significant figures are \(1\), \(0\), \(0\), \(0\), \(0\), \(0\)? No, that can't be. Wait, no, the correct rule is: For a number with a decimal point, all digits from the first non - zero digit to the last digit (including zeros at the end after the decimal) are significant. So in \(100.000\), the first non - zero digit is \(1\), then we have the two zeros before the decimal (wait, no, before the decimal, we have \(100\), and after the decimal, \(000\)). Wait, no, the number is \(100.000\), which is equal to \(1.00000\times10^{2}\). In scientific notation, \(1.00000\times10^{2}\) has six significant figures (the \(1\) and the five zeros? No, \(1.00000\) has six significant figures: \(1\), \(0\), \(0\), \(0\), \(0\), \(0\)? No, \(1.00000\) has six digits: \(1\), \(0\), \(0\), \(0\), \(0\), \(0\)? Wait, no, \(1.00000\) is \(1\) followed by five zeros after the decimal. So the significant figures are \(1\), \(0\), \(0\), \(0\), \(0\), \(0\)? No, each zero after the decimal in a number like \(1.00000\) is significant because the decimal is present. So \(1.00000\) has six significant figures. So \(100.000\) is the same as \(1.00000\times10^{2}\), so it has six significant figures.

Step2: Match with the options

The options are \(6\), \(3\), \(1\), \(5\). Since we determined that \(100.000\) has six significant figures, the correct option is \(6\).

Answer:

6