Question

which is the least: 0.06 or 0.060

Explanation:

Step1: Recall decimal place values

The first number is \(0.06\), which can be written as \(0.060\) (adding a trailing zero after the thousandths place doesn't change its value, as trailing zeros in the decimal part after the last non - zero digit don't affect the value of a decimal number). The second number is \(0.060\).

Step2: Compare the two decimals

Now we have two decimals: \(0.06 = 0.060\) and \(0.060\). So, we compare digit by digit. The tenths place: both have \(0\). The hundredths place: both have \(0\). The thousandths place: both have \(6\) (for \(0.06\) we can think of it as \(0.060\), so the thousandths place is \(6\)) and for \(0.060\) the thousandths place is \(6\), and the ten - thousandths place of \(0.060\) is \(0\), but since \(0.06\) is equivalent to \(0.060\), they have the same value. Wait, maybe there is a typo. If the second number is \(0.0060\) (maybe a mis - typing), let's assume that. If the numbers are \(0.06\) and \(0.0060\):

Step1 (corrected): Recall decimal place values

The number \(0.06\) means \(6\) hundredths or \(\frac{6}{100}=0.06\). The number \(0.0060\) means \(6\) thousandths or \(\frac{6}{1000} = 0.006\).

Step2 (corrected): Compare the two decimals

To compare \(0.06\) and \(0.006\), we can write them with the same number of decimal places. \(0.06=0.060\) and \(0.006 = 0.006\). Now, comparing the hundredths place: \(6\) (in \(0.060\)) vs \(0\) (in \(0.006\))? No, wait, the thousandths place: \(0\) (in \(0.060\) thousandths place? No, \(0.060\) is \(0\) tenths, \(0\) hundredths, \(6\) thousandths, \(0\) ten - thousandths. \(0.006\) is \(0\) tenths, \(0\) hundredths, \(0\) thousandths, \(6\) ten - thousandths? No, I made a mistake. Let's use the place value chart:

Place	Tenths	Hundredths	Thousandths	Ten - Thousandths
\(0.0060\)	\(0\)	\(0\)	\(6\)	\(0\)

Wait, no, \(0.06\) is \(0\) tenths, \(6\) hundredths, \(0\) thousandths, \(0\) ten - thousandths. \(0.006\) (or \(0.0060\)) is \(0\) tenths, \(0\) hundredths, \(6\) thousandths, \(0\) ten - thousandths. To compare, we look at the first non - zero digit from the left after the decimal. For \(0.06\), the first non - zero digit after decimal is in the hundredths place (\(6\) in hundredths place). For \(0.006\), the first non - zero digit after decimal is in the thousandths place (\(6\) in thousandths place). Since hundredths place is a higher place value than thousandths place, a digit in the hundredths place represents a larger value than the same digit in the thousandths place. So \(0.006\) (or \(0.0060\)) is less than \(0.06\).

Assuming the second number is \(0.0060\) (maybe a typo in the original problem, as \(0.06\) and \(0.060\) are equal). So if we assume the numbers are \(0.06\) and \(0.0060\), then \(0.0060\) is the least.

If the original numbers are \(0.06\) and \(0.060\), they are equal. But since the problem says "which is the least: \(0.06\) or \(0.060\)", maybe there is a typo. If we consider the numbers as given ( \(0.06\) and \(0.060\) ), they are equal. But if we assume a typo and the second number is \(0.0060\), then \(0.0060\) is less.

Assuming the problem has a typo and the second number is \(0.0060\):

Step1: Convert to same decimal places

\(0.06 = 0.0600\) and \(0.0060=0.0060\)

Step2: Compare digit by digit

• Tenths place: both \(0\)
• Hundredths place: \(6\) (for \(0.0600\)) vs \(0\) (for \(0.0060\))? No, wait, \(0.06\) is \(6\) hundredths (\(0.06=\frac{6}{100}\)), \(0.0060\) is \(6\) thousandths (\(0.0060 = \frac{6}{1000}\)). Since \(\frac{6}{1000}<\frac{6}{100}\) (because when the numerators are the same, the fraction with the larger denominator is smaller), so \(0.0060<0.06\).

Answer:

If the numbers are \(0.06\) and \(0.0060\) (assuming a typo), then \(0.0060\) is the least. If the numbers are \(0.06\) and \(0.060\) (as given), they are equal. But since the problem asks for the least, maybe there is a typo and the second number is \(0.0060\), so the least is \(0.0060\).