Secondary 1 Reading, Writing and Ordering Numbers

10 of the 11 questions

Each question targets one named concept from the sheet. Read them here, or print the PDF — it has working space under each one. 10 of the 11 questions are printed below. The other 1 is built on a diagram or a table of values that does not translate to the page, so it is in the free PDF — marked below where it would have come.

1. Q1Approximation and Rounding a Number

   A snow-clearing crew fills in its log at the end of a night shift. Round each reading as asked.

   1. The truck covered $47382$ m. Round to the nearest thousand metres.
   2. It spread $0.4675$ t of abrasive. Round to the nearest hundredth of a tonne.
   3. The last street took $12.96$ min. Round to the nearest tenth of a minute.
   4. It burned $38.5$ L of diesel. Round to the nearest ten litres.
2. Q2Ascending and Descending Order

   A weather station recorded six temperatures, in ${}^{\circ }\text{C}$: $$-3,2.5,-1.2,\frac{1}{2},\frac{9}{4},-0.75$$

   1. Write them in ascending order.
   2. Write them in descending order.
   3. Which reading is closest to $0{}^{\circ }\text{C}$?
3. Q3Decimal Notation

   Write each quantity in decimal notation.

   1. eight units and six hundredths
   2. $\frac{3}{4}$ of a litre
   3. ${\displaystyle \frac{17}{1000}}$
   4. $6+{\displaystyle \frac{2}{10}}+{\displaystyle \frac{9}{1000}}$
4. Q4Decomposing Numbers

   Follow the model $438=4\times 100+3\times 10+8\times 1$.

   1. Decompose $7046$.
   2. Decompose $52.83$.
   3. Rebuild the number described by $9\times 1000+4\times 10+6\times \frac{1}{100}$.
5. Q5Digits and Numbers
   1. How many digits are used to write $4077$? How many different digits?
   2. In $58124$, which digit occupies the hundreds position, and what is its value?
   3. Marc says: “$0$ is a digit, but it is not a number.” Is he right? Answer in one or two sentences.
6. Q6Expressing Numbers Using Different Types of Notation

   This question is built around a diagram or a table of values. Open it in the PDF.

7. Q7Number Positions and Values

   Consider the number $2607.058$.

   1. Name the position occupied by each digit that is not $0$.
   2. The digit $5$ appears once. What is its value?
   3. The number contains two $0$s. Explain what each one is doing, and say what the number would become if you simply erased it.
8. Q8Number Systems

   Our number system is positional and works in base ten. The Roman system is additive, with a subtractive shortcut for numbers such as $IV$ and $IX$.

   1. Write $2024$ in Roman numerals.
   2. Write the Roman numeral $MCDXLIX$ in our system.
   3. In $772$, the two $7$s do not have the same value. Explain why that can never happen in the Roman system.
9. Q9Ordering Decimal Numbers

   Six times, in seconds, from a school swim meet: $$31.8,31.08,30.9,31.75,30.85,31.5$$

   1. Rank the times from fastest to slowest.
   2. Insert $<$ or $>$: $31.08◻31.8$ and $30.9◻30.85$.
   3. Which time is closest to $31$ s?
10. Q10Writing Numbers
    1. Write $40208$ in words.
    2. Write “sixty thousand five hundred nine” in figures.
    3. Write $9.03$ in words.
    4. In a mathematics assignment, a student writes forty-two thousand as “$42,000$”. Which convention should be used in Québec, and how should the number be written?
11. Q11Synthesis — drawing on several sheets in this topic

    Five students measured the same hallway and reported $$12.4\text{ m},12.35\text{ m},12.5\text{ m},12.44\text{ m},12.6\text{ m}.$$

    1. Put the five measurements in ascending order.
    2. Each student now rounds their own measurement to the nearest tenth of a metre. Give the five rounded values.
    3. Three of the five reports become the same number. Explain how that happens, and say what is lost if the class orders the rounded values instead of the original ones.

The 9 challenge problems for this topic are a separate, paid sheet and are not reproduced here.

How to do every concept on this sheet

This is the part worksheet sites usually leave out. Below is the actual reasoning behind each group of questions — not a full solution set, the decisions that get you to one. Read it before you start, or after you get stuck.

A digit is not a value; a digit in a position is

The 7 in 772 is worth 700 and the 7 beside it is worth 70, and everything on this sheet follows from that one fact. Q7 makes it explicit: take a number with decimals in it, name the position each non-zero digit occupies, and say what one particular digit is worth — five hundredths, not five.

Decomposition is place value written out (Q4)

Writing 438 as 4 × 100 + 3 × 10 + 8 × 1 is a sentence saying what every digit is worth. Two things go wrong, and Q4 is built to catch both.

Rounding: one digit decides, and it is always the same one (Q1)

To round to a named place, look at the digit immediately to its right — that digit alone. Five or more rounds up, four or less leaves the place unchanged, and everything to the right of the place disappears. Q1 works through four different places on four different readings, including the case where rounding up carries: 12.96 to the nearest tenth becomes 13.0, because the 9 in the tenths goes up and spills into the units.

Ordering decimals, and the two reversals (Q2, Q9)

Comparing 31.8 with 31.08 by looking at which one has more digits gives the wrong answer, and the fix is mechanical: give every number the same number of decimal places first. Written as 31.80 and 31.08, the comparison is immediate.

Q2 adds two complications at once. Fractions appear among the decimals, so convert them all to one notation before ordering — one half is 0.5, nine quarters is 2.25 — and negatives appear, which reverses the rule most students are working from.

The same number, dressed differently (Q3, Q6)

Q3 writes quantities in decimal notation from words and from fractions; Q6 completes a table moving between fractional, decimal and percentage notation. (Q6 is built on a table, so it lives on the printed sheet rather than on this page.) The bridge in both directions is a denominator of 10, 100 or 1000: three quarters is seventy-five hundredths is 0.75 is 75%.

Why a positional system needs a zero at all (Q8)

Q8 sets our system beside the Roman one, which is additive: a symbol is worth the same amount wherever it is written, and the number is essentially the sum of its symbols. That is why the two 7s of 772 could never have different values in Roman numerals — and why an additive system needs no symbol for zero, since nothing in it is ever empty.

Positional notation buys brevity: ten digits write any number at all, and they write it short. The price is a symbol for an empty position, because without one, 3 048 and 348 would be the same string of digits in the same order. The zero is not a spare part of the system; it is what makes the system possible.

Writing numbers the way Québec writes them (Q10)

Digits are gathered into groups of three separated by a space, never a comma, and in English mathematics writing the decimal separator is a point. So forty-two thousand is written 42 000. Q10 also asks for numbers written out in words, which is where the zeros resurface: forty thousand two hundred eight names no thousands and no tens, and the words have to reflect that.

Q11: what rounding costs

The synthesis question has five students measure the same hallway and round their own measurements to the nearest tenth. Three of the five results collapse onto one number — and the question asks what is lost when the class orders the rounded values instead of the originals.

What is lost is the ordering itself: three students who were genuinely different can no longer be ranked, and a difference of several centimetres has vanished from the data. Rounding is a tool, and this question is where a student meets the cost of using it, which is a better lesson than any number of rounding drills.

Getting the most out of it

Say the number out loud, by position

“Two thousand six hundred seven, and fifty-eight thousandths.” Reading a number properly is most of the work of this topic: it forces you to place every digit, and it exposes a missing zero before it can cost you anything.

Pad decimals to the same length before comparing

Write 31.8 as 31.80 when it sits next to 31.08. Adding zeros on the right of a decimal changes nothing about its value, and it makes the comparison a matter of reading digit by digit rather than judging by eye.

Rebuild every decomposition

Add your own decomposition back up. If it does not return the number you started with, a position was skipped or a digit was given the wrong value — and you will find out in ten seconds rather than at the bottom of the page.

Common questions