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Understanding decimal place value is essential for reading and writing decimals accurately. In our number system, the position of a digit in a number determines its value. For decimals, each place or 'slot' to the right of the decimal point represents a fraction of ten. The first digit to the right of the decimal point is in the 'tenths' place, meaning it is ten times smaller than 'ones'.

The second digit is in the 'hundredths' place (ten times smaller than the 'tenths'), and the third is in the 'thousandths' place (ten times smaller than the 'hundredths').

When writing a decimal like \(0.004\), we see that there are no tenths or hundredths, only thousandths. The zeroes indicate that those places are empty and it's the 4 in the thousandths place that counts. So, the place value of the digit 4 here is 'four thousandths'.

Mathematical notation is a language that uses symbols and numbers to represent mathematical objects, operations, relations, and formulas. In the context of decimals, we use a period or dot – known as the decimal point – to separate whole numbers from the fractional part.

This notation helps us to be precise about which place value we're referring to. In \(0.004\), the notation indicates that 4 is in the third place after the decimal, emphasizing its placement in the thousandths place. This clarity in notation is crucial for understanding and conveying the exact value of numbers in mathematics.

Break It Down

When reading decimals, it helps to break them down by place value. Consider our example \(0.004\). Starting from the decimal point, count each place until you reach the non-zero digit. Each 'hop' represents a power of ten:

• 'Tenths' for the first hop,
• 'Hundredths' for the second,
• 'Thousandths' for the third.

Since we have three hops before we get to the digit 4, we say 'four thousandths'.

No Leading Zero

It's important not to include the leading zero before the decimal point when reading decimals aloud. The leading zero does not add value and can be misleading when communicating the number verbally. Thus, we don't say 'zero and four thousandths'; we simply say 'four thousandths'.