Math // Fractions

Converting tenths to hundredths

Express a fraction with denominator 10 as an equivalent fraction with denominator 100 and use this to add fractions with denominators 10 and 100 (e.g. 3/10 + 4/100 = 34/100)

Ages
9 to 10
Type
Method
Builds on
2 topics
Leads to
1 topic
Standards
1 code

Quick check

If the learner needs to add 3/10 and 17/100, can they rewrite 3/10 as hundredths first — and then add the two fractions together?

Ask this to see whether the topic is secure.

Topic // Mastery

What mastery looks like

What a learner can do once this topic is secure.
  • Rewrite 7/10 as 70/100
  • Calculate 3/10 + 4/100 = 34/100
  • Explain why 5/10 = 50/100 using a hundredths grid

Topic // Map

Where this fits

What to learn first and what this topic opens up, with the reason for each link. Required links come first.
  • RequiredMust come first
  • HelpfulHelps, but not essential

Before this

2 topics
  • Tenths (age 8+)Required

    Fractions // Ages 8 to 9

    Understanding hundredths is prerequisite to working with 10ths and 100ths together

  • Equivalent fractions (age 9+)Required

    Fractions // Ages 9 to 10

    Generating equivalent fractions supports converting 10ths to 100ths

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Converting tenths to hundredths

Ages 9 to 10 // Method

Leads to

1 topic

Topic // Research-informed

Teaching notes

From the Marble Skill Taxonomy. These notes have not been validated in classrooms, so treat them as a starting point for your own judgement.

The approach

Converting tenths to hundredths rests on place value and the equivalent-fraction principle (×10/×10): one tenth is ten hundredths, so 3/10 = 30/100, and 3/10 + 4/100 becomes 30/100 + 4/100 = 34/100. Learners cannot combine tenths and hundredths until the pieces are the same size, so the conversion must happen before adding. A 10×10 hundredths grid (each column = one tenth = ten small squares) makes this relationship concrete; a base-ten flat/rod model, place-value columns, number lines, money (£0.30 = 30p) and metric (3/10 m = 30 cm) anchor it in familiar units, and the decimal form (34/100 = 0.34) bridges to decimal notation.

Common misconceptions

  • Adds across both denominators: 3/10 + 4/100 = 7/110 (adds tops and bottoms)
  • Treats 3/10 as 3 hundredths, shading three single squares, and reports 7/100
  • Thinks the denominators can be added because 'they are close', ignoring that the pieces are different sizes

Useful representations

  • 10×10 hundredths grid (column = tenth, square = hundredth)
  • Place-value chart with tenths and hundredths columns
  • Number line 0–1 marked in hundredths
  • Base-ten flat/rod (rod = tenth of the flat, small cube = hundredth)

Teaching practices

  • Anchor every conversion on a 10×10 hundredths grid: one full column of ten small squares is one tenth, making '1 tenth = 10 hundredths' visible rather than a rule
  • Convert BEFORE combining — shade the tenths as whole columns, then the extra hundredths as single squares, then count all the small squares
  • Connect to place-value columns (tenths | hundredths) and to money/metric (£0.30 = 30p, 3/10 m = 30 cm) so the ×10 relationship is felt in familiar units
  • Insist the answer is read back in hundredths and, when ready, as a decimal (34/100 = 0.34) to bridge to decimal notation
  • Contrast a correct conversion with the '7/110' error out loud so children can articulate why you never add the denominators

Activities to try

  1. 1

    Build 3/10 + 4/100 on a hundredths grid

    Why it works: Three tenths covers the same shaded area as thirty hundredths, so tenths must be converted to hundredths before they can be added to hundredths.

    1. Take a blank 10×10 hundredths grid where each full column of ten small squares represents one tenth.
    2. Shade 3/10 by filling three whole columns, then count the small squares covered to confirm it is 30 hundredths.
    3. Add 4/100 by shading four more single squares.
    4. Count all the shaded small squares and report the total as hundredths (34/100), then, when ready, write it as a decimal (0.34).
    5. Deliberately try shading just three lone single squares for 3/10 first, notice that this is only 3/100, then correct it to three full columns.
  2. 2

    Explain why 5/10 = 50/100 and challenge the 7/110 error

    Why it works: Equivalent tenths-to-hundredths conversions come from multiplying numerator and denominator by ten; denominators are never added because they name the size of the pieces, which must match before combining.

    1. On a hundredths grid, show 5/10 and explain why it covers 50 small squares, not 5.
    2. Rewrite 7/10 as an equivalent fraction over 100 (70/100).
    3. Respond to a classmate who claims 3/10 + 4/100 = 7/110: explain out loud why you never add the denominators, using the idea that the pieces are different sizes until converted.
    4. When offered answer choices such as 34/100, 7/110 and 7/100, pick 34/100 and say explicitly why each of the other two is wrong.
    5. Sort several sums into 'already hundredths' versus 'convert a tenth first' before solving them.
  3. 3

    Connect to place value, money and metric, then to decimals

    Why it works: The tenth-to-hundredth ×10 relationship is the same structure seen in place value, money and metric measures, and it bridges directly to decimal notation.

    1. Place tenths and hundredths into a place-value chart with labelled tenths and hundredths columns and read the conversion from the columns.
    2. Match each fraction to a familiar unit: 3/10 = £0.30 = 30p, and 3/10 m = 30 cm, noting the ×10 relationship.
    3. Mark 0.34 on a 0–1 number line divided into hundredths and relate it to 34/100.
    4. Write a converted answer such as 34/100 as the decimal 0.34 and say why they are the same quantity.
    5. Transfer to a fresh pair, e.g. 6/10 + 7/100 (= 67/100), aiming to convert without needing the grid.

Topic // Standards

Curriculum standards

Codes for the curriculum statements this topic maps to. Each publisher owns its standard text.
Common Core State Standards for Mathematics
4.NF.5

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