Fractions to decimals in 4th grade

Point P is at $0.7$, but the target is $0.3$ — P is in the wrong tenth interval.

1. 1Look at the number line. It is divided into tenths between $0.0$ and $1.0$. Each tick mark is one tenth, or $0.1$.
2. 2Find where $0.3$ should be. Starting from $0.0$, count three ticks to the right: $0.1$, $0.2$, $0.3$. The target sits at the third tick.
3. 3Now find where Liam placed point P. Counting from $0.0$, P lands on the seventh tick — that is $0.7$. Since $0.7$ is in the interval from $0.7$ to $0.8$, and $0.3$ is in the interval from $0.3$ to $0.4$, P is in the wrong tenth interval.

Common mistake. A common mistake is comparing only the digit names instead of counting tenths from $0.0$ — always count each tick carefully to find the exact tenth where P sits.

The idea underneath. On a tenths number line, every tick equals $0.1$. To check a plotted decimal, count the ticks from $0.0$ to find the exact tenth where the point sits, then compare it to the target.

The numerator should be $3$, not $4$. To equal $0.3$, the fraction is $\frac{3}{10}$.

1. 1First, find the correct fraction for $0.3$. The decimal $0.3$ means $3$ tenths, so the fraction with denominator $10$ is $\frac{3}{10}$.
2. 2Compare Aiden's work to the correct fraction.
3. 3The denominator $10$ is correct, but the numerator is wrong. Aiden wrote $4$, but the digit after the decimal point in $0.3$ is $3$. So the numerator should be $3$, not $4$.

Common mistake. A common mistake is misreading the digit after the decimal point. The numerator should always be the digit that comes after the decimal point. In $0.3$, that digit is $3$, so the numerator must be $3$, not $4$.

The idea underneath. When a decimal has one digit after the decimal point, that digit becomes the numerator and 10 is the denominator.

The shaded part is 0.14, because 14 out of 100 squares are shaded.

1. 1Look at the grid below. It is divided into 100 small squares (10 rows of 10). Count how many squares are shaded blue.
2. 2There is $1$ complete row shaded. Each row has $10$ squares, so the complete row gives $1 \times 10 = 10$ shaded squares.
3. 3In the next row, $4$ more squares are shaded. Add these to the $10$ from the complete row: $10 + 4 = 14$ shaded squares in all.
4. 4$14$ out of $100$ squares is written as the decimal $0.14$ — that is, $14$ hundredths.

Common mistake. A common mistake is counting only the 1 complete shaded row and writing 0.10, forgetting to add the 4 extra shaded squares in the next row.

The idea underneath. When 100 small squares make one whole, each shaded square is one hundredth (0.01). So 14 shaded squares means 14 hundredths, written as 0.14.

Answer. 5

The mixed number is $12\frac{5}{100}$. Keep the denominator $100$ — do not simplify.

1. 1The decimal $12.05$ has a whole-number part and a fractional part. The whole-number part is $12$ (the digits before the decimal point).
2. 2The fractional part is $0.05$. Count the digits after the decimal point: there are $2$ digits ($0$ and $5$), so the denominator is $100$ (hundredths).
3. 3Write the fractional part as a fraction with denominator $100$. The two-digit string after the decimal point is $05$, which equals the integer $5$:
4. 4Combine the whole-number part and the fraction to get the mixed number:

Common mistake. A common mistake is to write $12\frac{50}{100}$ instead of $12\frac{5}{100}$. The digit just after the decimal point is $0$, so the fractional string is $05 = 5$, not $50$. Reading the digits in the wrong order reverses the numerator.

The idea underneath. The number of digits after the decimal point tells you the denominator: $1$ digit means tenths (denominator $10$), and $2$ digits means hundredths (denominator $100$).