The Tenths Place

The first decimal position counts tenths

The tenths place is the first digit immediately to the right of the decimal point. One tenth is one of ten equal parts of a whole and is written 0.1. This is the structure to keep in mind before choosing a calculation or rewriting the number.

Point to the first decimal digit, name its place, then interpret it as that many tenths. If later digits exist, keep them visible when reading the complete number. Make a quick estimate or identify the relevant unit first; that gives you a check independent of the written steps.

A digit’s value is found by multiplying the digit by the unit of its column. In 4.7 = 4 + 7/10, a 6 in the tenths place contributes 0.6, while a 6 in the hundredths place contributes 0.06. The digit is the same; its position changes the amount by a factor of ten.

Applying the tenths place in context

A distance of 4.7 kilometres means four kilometres plus seven tenths of a kilometre. Since one kilometre contains 1000 metres, the fractional part equals 700 metres.

Expand 4.7 = 4 + 7/10 into the amounts contributed by its digits, then add those amounts back together. This checks the place names and catches a zero that was skipped or put in the wrong column.

Classify the zeros in 4.7 = 4 + 7/10 by their role. A leading zero shows there are no whole units, an internal zero can hold a place, and a trailing zero can show precision without changing value. That role determines whether removing a zero preserves the number.

Why the tenths place works

Place value follows a base-ten pattern: each move left multiplies a place by ten, and each move right divides it by ten. In 4.7 = 4 + 7/10, a digit’s contribution is its digit multiplied by the value of its column. The decimal point separates whole units from fractional units; it is not itself a digit.

Zeros can hold a place without adding an amount. In 4.7 is four and seven tenths., check whether each zero keeps a later digit in its intended column. Writing the number as a sum of its nonzero place values is a useful way to test both the column names and the total.

Expanded form checks the columns one at a time. Write 4.7 = 4 + 7/10 as a sum of its nonzero digit values, such as whole units plus tenths plus hundredths, then add those terms. If the sum changes the number, a digit was assigned to the wrong place or a placeholder was missed.

Explore a nearby the tenths place case

Move one nonzero digit in 4.7 = 4 + 7/10 a single column to the left, then to the right. Its value should become ten times as large in the first move and one tenth as large in the second.

After moving a digit in 4.7 = 4 + 7/10, rebuild the changed number in expanded form. If the sum does not match the numeral, inspect the place name and any zero holding a later digit in position.

Questions to test the tenths place

Use these questions after finishing a problem about tenths place:

• Which column gives the selected digit its value in 4.7 = 4 + 7/10?
• Is any zero holding a later digit in its place?
• Could expanded form rebuild the original decimal?

Check a the tenths place result

Before you accept a result, pause and ask:

• Name the column as well as the digit.
• Check every placeholder zero.
• Expand the number into digit values.
• Add the parts to confirm 4.7 = 4 + 7/10.