The concept of a decimal number

State the place value (units, tenths, hundredths or thousandths) of the digit $7$ in each of the following numbers:

1. a) $15,72$
2. b) $0,007$
3. c) $7,431$
4. d) $2,075$

Expand the following decimal numbers according to their place value units, as in the example:

Example: $4,25 = 4$ Units + $2$ tenths + $5$ hundredths.

1. a) $8,39$
2. b) $12,045$
3. c) $0,614$

Complete these equivalences between place values:

1. a) $4$ units = ____ tenths.
2. b) $70$ hundredths = ____ tenths.
3. c) $5$ tenths = ____ thousandths.
4. d) $300$ thousandths = ____ hundredths.

Copy into your notebook and use the symbols $<$ or $>$ to compare these pairs of decimal numbers:

1. a) $5,4$ ____ $5,39$
2. b) $0,25$ ____ $0,3$
3. c) $12,07$ ____ $12,071$
4. d) $6,1$ ____ $6,099$

In the school Olympics, the times recorded in the $100$ metres flat final were very close. The judges recorded the following results in seconds:

$12,45$ — $12,408$ — $12,5$ — $12,099$ — $12,41$

Order the runners from fastest (shortest time) to slowest (longest time) using the symbol $<$ and write out in words the decimal number that corresponds to the gold medal winner.

Lucía is packing her rucksack for a trip. She has bought a bottle of water for $1,25$ €, a bag of nuts for $3,050$ € and a cap for $9,9$ €.

1. a) Write all the prices so that they have the same number of decimal places (adding zeros if necessary).
2. b) Convert the price of the cap into an irreducible fraction.
3. c) How many euro cents does the bag of nuts cost?

Match each decimal number with its corresponding decimal fraction:

• Numbers: $0,7$ | $0,07$ | $7,7$ | $0,77$

• Fractions: $\frac{77}{100}$ | $\frac{7}{10}$ | $\frac{7}{100}$ | $\frac{77}{10}$

If we divide a square into $100$ equal parts, each part is one hundredth ($0,01$). Look at the following image and write which decimal number represents the orange shaded area:

Classify the following decimal numbers, indicating whether they are terminating decimals, pure recurring decimals or mixed recurring decimals. For recurring decimals, clearly state what the recurring part is and, if present, the non-recurring part:

1. a) $5,08$
2. b) $2,333...$
3. c) $14,252525...$
4. d) $0,1666...$
5. e) $3,141592...$ (is this last one a recurring decimal number?)

Sometimes fractions help us better understand the type of decimal number we have. Without performing long division, classify the decimal expansion of the following fractions as terminating or recurring:

1. a) $\frac{7}{20}$
2. b) $\frac{4}{9}$
3. c) $\frac{13}{6}$
4. d) $\frac{1}{25}$