Decimals — place value, conversions and operations

In 5 839.264, the decimal point separates the whole number (5 839) from the decimal part (.264).

Moving right from the decimal point: the first place is tenths, the second is hundredths, the third is thousandths.

In .264: the digit 2 is in the tenths place, the digit 6 is in the hundredths place, and the digit 4 is in the thousandths place.

The digit 6 is in the hundredths position, so its place value is $\frac{6}{100}=0.06$.

We need the place value of the digit 6 in 5 839.264.

Tenths is the first position after the decimal point. In 5 839.264, the digit in the tenths place is 2, not 6. Eliminate this option.

Thousandths is the third position after the decimal point. In 5 839.264, the digit there is 4. Eliminate this option.

Tens is a whole-number place to the left of the decimal point (the 3 in 5 839). The digit 6 is to the right of the decimal, so this is eliminated.

The only remaining option is Hundredths, which is correct — 6 is the second digit after the decimal point, worth $\frac{6}{100}$.

To convert a decimal to a percentage, multiply by 100 and add the % symbol. This moves the decimal point 2 places to the right.

$0.35\times 100=35$

Adding the % symbol: $0.35=35\%$.

Converting a decimal to a percentage means multiplying by 100 — moving the decimal point 2 places to the right.

3.5% would mean moving the decimal only 1 place right ($0.35\times 10=3.5$). That is multiplying by 10, not 100. Eliminate.

350% would mean multiplying by 1000 ($0.35\times 1000=350$). We need to multiply by 100, not 1000. Eliminate.

0.0035% is far too small — it results from dividing instead of multiplying. This is the opposite of what we need. Eliminate.

35% is correct: $0.35\times 100=35$, so $0.35=35\%$.